"Now analysis is of two kinds, the one directed to searching for the truth and called theoretical, the other directed to finding what we are told to find and called problematical. (1) In the theoretical kind we assume what is sought as if it were existent and true, after which we pass through its successive consequences, as if they too were true and established by virtue of our hypothesis, to something admitted: then (a), if that something admitted is true, that which is sought will also be true and the proof will correspond in the reverse order to the analysis, but (b), if we come upon something admittedly false, that which is sought will also be false. (2) In the problematical kind we assume that which is propounded as if it were known, after which we pass through its successive consequences, taking them as true, up to something admitted: if then (a) what is admitted is possible and obtainable, that is, what mathematicians call given, what was originally proposed will also be possible, and the proof will again correspond in reverse order to the analysis, but if (b) we come upon something admittedly impossible, the problem will also be impossible."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
Pappus, (c. 330 AD) as quoted by Thomas Little Heath, The Thirteen Books of Euclid's Elements (1908) Vol. 1, Ch. IX. §6.
https://en.wikiquote.org/wiki/Analysis
Revision History
No revisions have been submitted for this quote.
Categories
Analysis
20 quotes on TrueQuotesView all quotes by Analysis →
Related Quotes
"My work in the future must be devoted entirely to pure mathematics in its abstract meaning. I shall apply all my stre…"
"Philosophers hasten too much from the analytic to the synthetic method; that is, they draw general conclusions from t…"
"The terms synthesis and analysis are used in mathematics in a more special sense than in logic. In ancient mathematic…"
"The idea that God may be approached and understood through intellectual analysis is uniquely Christian. ...It is prob…"
"The oldest definition of Analysis as opposed to Synthesis is that appended to Euclid XIII. 5. It was possibly framed …"
"Analysis and synthesis, though commonly treated as two different methods, are, if properly understood, only the two n…"
"The Mss. [of Euclid’s Elements] contain a curious addition to XIII. I-5 in the shape of analyses and syntheses for ea…"
"Vieta presented his analytic art as "the new algebra" and took its name from the ancient mathematical method of "anal…"
"Fortunately analysis is not the only way to resolve inner conflicts. Life itself still remains a very effective thera…"
"Analysis and natural philosophy owe their most important discoveries to this fruitful means, which is called inductio…"